Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 2$ and $ BC = 5x + 4$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 2} = {5x + 4}$ Solve for $x$ $ 3x = 6$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({2}) - 2$ $ BC = 5({2}) + 4$ $ AB = 16 - 2$ $ BC = 10 + 4$ $ AB = 14$ $ BC = 14$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {14} + {14}$ $ AC = 28$